CINCINNATI -- Center fielder Carlos Gomez and the last-place Milwaukee Brewers are finding their swagger.

On Friday night, Gomez hit a grand slam and drove in five runs and Mike Fiers allowed three hits in seven innings, lifting the Brewers to a 12-1 victory over the Cincinnati Reds at sold-out Great American Ball Park.

Left fielder Gerardo Parra and third baseman Aramis Ramirez added solo homers for Milwaukee (34-48), which has won six straight games, its longest winning streak since April 2014.

Catcher Jonathan Lucroy and right fielder Ryan Braun each had three hits, including a double and an RBI to pace the Brewers' 16-hit outburst.

"Everybody knows this is a dangerous lineup," Gomez said. "When you combined speed and power and really good hitting, we're going to make a lot of runs. All 30 teams know that. The whole year we haven't put it together like we have now. We expect that."

Milwaukee was coming off a four-game sweep at Philadelphia when it batted .364 and scored 28 runs. The Brewers rode took that momentum to Cincinnati.

"It's been contagious," Milwaukee manager Craig Counsell said. "Guys have gotten going. It's good to see, and fun to watch."

The Brewers already were leading 5-0 in the seventh when Gomez crushed a 1-0 pitch from right-hander Carlos Contreras for his first career grand slam and his sixth homer this season.

"The at-bat before that I hit a good line drive through the middle so I wanted to follow that approach," Gomez said. "He threw me a changeup. I didn't hit it that good, but it went out."

Fiers (4-7) was in control throughout, allowing one Reds runner to advance past first base, and that came on his throwing error in the seventh.

His outing was in stark contrast to the last time Fiers faced Cincinnati on April 21 when he allowed eight runs (four earned) in a 16-10 loss at Miller Park.

"My changeup was really good today," Fiers said of his first career win at Great American Ball Park. "My changeups were big because later in the game they started zoning in on the fastball and trying to jump me."

Right-hander Michael Lorenzen (3-3) was impressive in his first 13 appearances. But he struggled on Friday night for Cincinnati (36-42), allowing three earned runs and five hits.

"Michael got a lot of his hard stuff up against a hot hitting team," Reds manager Bryan Price said. "Sometimes when you have good stuff like his, you can get by when they foul off those pitches. They got his pitch count up and took advantage of our bullpen."

Milwaukee scored first when Parra launched a 2-2 pitch from Lorenzen an estimated 389 feet for his seventh career leadoff home run and his second this season.

The Brewers increased their lead to 3-0 on Ramirez's 10th home run, a 419-foot blast on Lorenzen's first pitch in the second.

Lorenzen struggled with his command, throwing 90 pitches through four innings.

"That's a really good team. They had a couple of good series coming in," Lorenzen said. "I could have done better with my pitch selection. When you don't throw with conviction, this happens. You learn from it."

Fiers allowed two hits and a walk through four innings.

"His past two starts have been really, really good," Counsell said. "Tonight was his best one."

In the fifth, an RBI double by Lucroy and an RBI single by Gomez, both against right-hander Nate Adcock, made the score 5-0.

Fiers got some defensive help in the fourth when shortstop Jean Segura made a diving catch of third baseman Todd Frazier's liner leading off the inning and Ramirez dived to his right to snag shortstop Eugenio Suarez's grounder to end the inning.

Then Fiers helped himself with a lunging catch of second baseman Brandon Phillips' foul pop against the home dugout railing in the sixth.

"In that situation, you're going to do anything you can to make a play," Fiers said. "I was glad I made the catch and got a big out there."

NOTES: In eight meetings this season, the Reds (15) and Brewers (14) have combined for 29 home runs. ... Reds assistant hitting coach Lee Tinsley was placed on administrative leave Friday after his arrest on Thursday for driving while impaired. "We're in the fact-finding stage right now; it'll take some time," manager Bryan Price said. ... Reds LHP Tony Cingrani began a rehabilitation stint at Triple-A Louisville on Friday. He has been on the disabled list since June 15 with a strained left shoulder. ... The Brewers recalled RHPs Tyler Cravy and David Goforth from Triple-A Colorado Springs on Friday and optioned INF/OF Jason Rogers and RHP Corey Knebel to the Sky Sox. ... Milwaukee's five-game winning streak equaled its longest since Aug. 14-19 of last season.